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3 years ago

If A, B, and C are the vertices of a triangle, find AB + BC + CA.

Mathematics

1 answer:

iVinArrow [24]3 years ago

5 0

Answer:

Step-by-step explanation:

When drawing a triangle, note that the vectors can be drawn either in a clockwise or anticlockwise direction. For a triangle with vertices A, B and C, te vectors are AB, BC and CA

In vector notation CA = - AC (length CA is equal to AC but acting in opposite direction to AC)

and AB+BC = AC

To evaluate AB + BC + CA, we will substitute the vector expression above into the given expression and simplify as shown;

= (AB + BC) + CA

= AC + (-AC)

open the parenthesis

= AC-AC

= 0

<em>Hence the sum of the vector expression AB + BC + CA is a zero vector</em>

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You are to take a multiple-choice exam consisting of 64 questions with 5 possible responses to each question. Suppose that you h

damaskus [11]

Answer:

a) Expected score on the exam is 12.8.

b) Variance 10.24, Standard deviation 3.2

Step-by-step explanation:

For each question, there are only two possible outcomes. Either you guesses the answer correctly, or you does not. The probability of guessing the answer of a question correctly is independent of other questions. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The expected value of the binomial distribution is:

$E(X) = np$

The variance of the binomial distribution is:

$V(X) = np(1-p)$

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

64 questions.

So $n = 64$

5 possible answers, one correctly, chosen at random:

So $p = \frac{1}{5} = 0.2$

(a) What is your expected score on the exam?

$E(X) = np = 64*0.2 = 12.8$

(b) Compute the variance and standard deviation of x. Variance =Standard deviation

$V(X) = np(1-p) = 64*0.2*0.8 = 10.24$

Variance 10.24

$\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{64*0.2*0.8} = 3.2$

Standard deviation 3.2

5 0

3 years ago

What is the ruler postulate

ch4aika [34]

Answer:

The points on a line can be assigned real number coordinates (think of numbers on a number line). The distance between any two points is their difference.

3 0

3 years ago

Suppose the heights of a population of people are normally distributed with a mean of 65.5 inches and a standard deviation of 2.

kupik [55]

Answer:

a) $P(64.2$

b) 69.764

Step-by-step explanation:

1) Previous concepts

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".

2) Part a

Let X the random variable that represent the heights of a population, and for this case we know the distribution for X is given by:

$X \sim N(65.5,2.6)$

Where $\mu=65.5$ and $\sigma=2.6$

We are interested on this probability

$P(64.2$

And the best way to solve this problem is using the normal standard distribution and the z score given by:

$z=\frac{x-\mu}{\sigma}$

If we apply this formula to our probability we got this:

$P(64.2$

And we can find this probability on this way:

$P(-0.50$

And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.

$P(-0.50$

3) Part b

For this part we want to find a value a, such that we satisfy this condition:

$P(X>a)=0.05$ (a)

$P(X$ (b)

Both conditions are equivalent on this case. We can use the z score again in order to find the value a.

As we can see on the figure attached the z value that satisfy the condition with 0.95 of the area on the left and 0.05 of the area on the right it's z=1.64. On this case P(Z<1.64)=0.95 and P(z>1.64)=0.05

If we use condition (b) from previous we have this:

$P(X$